A hierarchy of local decision
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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17
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Theoretical Computer Science, Volume 856, pp. 51-67
Abstract
We extend the notion of distributed decision in the framework of distributed network computing, inspired by both the polynomial hierarchy for Turing machines and recent results on so-called distributed graph automata. We show that, by using distributed decision mechanisms based on the interaction between a prover and a disprover, the size of the certificates distributed to the nodes for certifying a given network property can be drastically reduced. For instance, we prove that minimum spanning tree (MST) can be certified with O(logn)-bit certificates in n-node graphs, with just one interaction between the prover and the disprover, while it is known that certifying MST requires Ω(log2n)-bit certificates if only the prover can act. The improvement can even be exponential for some simple graph properties. For instance, it is known that certifying the existence of a nontrivial automorphism requires Ω(n2) bits if only the prover can act. We show that there is a protocol with two interactions between the prover and the disprover that certifies nontrivial automorphism with O(logn)-bit certificates. These results are achieved by defining and analyzing a local hierarchy of decision which generalizes the classical notions of proof-labeling schemes and locally checkable proofs.Description
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Feuilloley, L, Fraigniaud, P & Hirvonen, J 2021, 'A hierarchy of local decision', Theoretical Computer Science, vol. 856, pp. 51-67. https://doi.org/10.1016/j.tcs.2020.12.017